A Shift-Dependent Generalized Doubly Truncated (Interval) Information Measure and its Properties

Bilal Ahmad Bhat¹ , M.A.K. Baig²

Section:Research Paper, Product Type: Isroset-Journal
Vol.6 , Issue.1 , pp.282-293, Feb-2019

CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v6i1.282293

Online published on Feb 28, 2019

Copyright © Bilal Ahmad Bhat, M.A.K. Baig . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
 

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Abstract :
In the present article, we develop a two parametric shift-dependent generalized interval information (uncertainty) measure. In this new measure, the length of the observed random variable is set as the weight function and hence it is also known as length-biased shift-dependent uncertainty measure. Some significant characterization results of this measure are focused. For the measure, several momentous properties are also explored. Finally, we present some upper and lower bounds of this particular measure.

Key-Words / Index Term :
Shift-dependent generalized entropy, Lifetime distributions, Shift-dependent generalized interval entropy, Characterization results

References :
[1] C. E. Shannon, “A mathematical theory of communications”, Bell System Technical Journal, 27, pp. 379-423, 1948.
[2] N. Ebrahimi, “How to measure uncertainty in the residual lifetime distribution”, Sankhya Series A, 58, pp. 48-56, 1996.
[3] S. M. Sunoj, P. G. Sankaran and S. S. Maya, “Characterizations of life distributions using conditional expectations of doubly (interval) truncated random variables”, Communications in Statistics—Theory and Methods, 38 (9), pp. 1441–1452, 2009.
[4] M. Belis and S. Guiasu, “A quantitative-qualitative measure of information in cybernetic systems”, IEEE Transactions on Information Theory, IT, 4, pp. 593–594, 1968.
[5] Di Crescenzo and M. Longobardi, “On weighted residual and past entropies”, Scientiae Mathematicae Japonicae, 64, pp. 255–266, 2006.
[6] F. Misagh and G. H. Yari “On weighted interval entropy”, Statistics and Probability Letters, 81, pp. 188–194, 2011.
[7] M. Mirali and S. Baratpour, “Dynamic version of weighted cumulative residual entropy”, Communications in Statistics-Theory and Methods, 46, 2017.
[8] F. Misagh, Y. Panahi, G. H.Yari and R. Shahi, “Weighted cumulative entropy and its estimation”, In Quality and Reliability (ICQR), IEEE International conference, pp. 477-480, 2011.
[9] S. Kayal, “On weighted generalized cumulative residual entropy”, Springer Science+Business Media New York, pp. 1-17, 2017.
[10] R. S. Nair, E. I. A. Sathar and G. Rajesh, “A study on dynamic weighted failure entropy of order ”, American Journal of Mathematical and Management Sciences, 36(2), pp. 137-149, 2017.
[11] M. Nourbakhsh and G. Yari, “Weighted Renyi’s entropy for lifetime distributions”, Communications in Statistics-Theory and Methods, doi: 10.1080 /03610926.2016.1148729, 2016.
[12] Y. Shiwei and H. Ting-Zhu, “Exponential weighted entropy and exponential weighted mutual information”, Neurocomputing, 249, pp. 86–94, 2017.
[13] H. Khammar and S. M. A. Jahanshahi, “On weighted cumulative residual Tsallis entropy and its dynamic version”, Physica A, 491, pp. 678–692, 2018.
[14] S. Yasaei Sekeh, G. R. Mohtashami Borzadaran and , A. H. Rezaei Roknabadi, “Some results based on weighted dynamic entropies”, Rend. Sem. Mat. Univ. Politec. Torino, Vol. 70, 4, pp. 369 – 382, 2012.